Is the inductive limit of tensor product $L^{\infty}(X,\mu)^{\otimes \infty}$ is isomorphic to $L^{\infty}(X,\mu)$?
2026-03-26 10:07:09.1774519629
Some clarifications required
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No. Take $X = \{0,1\}$ with $\mu(0) = \mu(1) = 1/2$, its infinite tensor product is diffuse.